A google duel involves the use of the google search engine in order to resolve the conflict in question, and it usually ends with the loser being owned and/or tea bagged.
Guy #2: No, it's not; it's Sacramento
Guy #1: Fine, I challenge you to a google duel (looks it up via google)
Guy #2: ...See, told you so. Dude, I just owned your ass!
Guy #1: ... shit.